Question

Let \(f:\R→\R\) be a function defined by
\(f(x) = \begin{cases}     x^2\sin(\frac{\pi}{x^2}), & \text{if } x \ne 0, \\     0, & \text{if } x = 0. \end{cases}\)
Then which of the following statements is TRUE ?

• A. f(x) = 0 has infinitely many solutions in the interval \([\frac{1}{10^{10}},\infin)\)
• B. f(x) = 0 has no solutions in the interval \([\frac{1}{\pi},\infin).\)
• C. The set of solutions of f(x) = 0 in the interval \((0,\frac{1}{10^{10}})\) is finite.
• D. f(x) = 0 has more than 25 solutions in the interval \((\frac{1}{\pi^2},\frac{1}{\pi})\)

Answer 1

The Correct Option is D

The correct option is (D):f(x) = 0 has more than 25 solutions in the interval \((\frac{1}{\pi^2},\frac{1}{\pi})\).